Improved Efficient Projection Density Function Based on Topology Optimization

Topology optimization is a powerful tool having capability of generating new solution to engineering design problems, while these designs enhance manufacturability and reduce manufacturing costs in a computational setting. Mesh-independent convergence and other techniques have been widely used as topology optimization technique, but they produce gray transition regions which is not a favorable condition for any material. In this article, a modified topology optimization formulation using a new function has been proposed. The suggested scheme makes use of the Heaviside Projection Method (HPM) to continuum topology optimization. Such technique is helpful to obtain the minimum length scale influence on void and solid phases. Application of this proposed approach is implemented to obtain the minimum compliance for macrostructures. Numerical remarkable examples illustrate the noteworthy value of the proposed approach.

An approach for geometrically nonlinear topology optimization using moving wide-Bézier components with constrained ends

Standard moving morphable component (MMC)-based topology optimization methods use free components with explicitly geometrical parameters as design units to obtain the optimal structural topology by moving, deforming and covering such components. In this study, we intend to present a method for geometrically nonlinear explicit topology optimization using moving wide Bezier components with constrained ends. Not only can the method efficiently avoid the convergence issues associated with nonlinear structural response analysis, but it can also alleviate the component disconnection issues associated with the standard MMC-based topology optimization methods. The numerical investigations proposed in this work indicate that the proposed method allows us to obtain results in accordance with the current literature with a more stable optimization process. In addition, the proposed method can easily achieve minimum length scale control without adding constraints.

Revisiting the minimum length in the Schwinger–Keldysh formalism

The existence of a minimum length in quantum gravity is investigated by computing the in-in expectation value of the proper distance in the Schwinger–Keldysh formalism. No minimum geometrical length is found for arbitrary gravitational theories to all orders in perturbation theory. Using non-perturbative techniques, we also show that neither the conformal sector of general relativity nor higher-derivative gravity features a minimum length. A minimum length scale, on the other hand, seems to always be present when one considers in-out amplitudes, from which one could extract the energy scale of scattering processes.

Optimizing Topology and Fiber Orientations With Minimum Length Scale Control in Laminated Composites

Discrete material optimization (DMO) has proven to be an effective framework for optimizing the orientation of orthotropic laminate composite panels across a structural design domain. The typical design problem is one of maximizing stiffness by assigning a fiber orientation to each subdomain, where the orientation must be selected from a set of discrete magnitudes (e.g., 0 deg, ±45 deg, 90 deg). The DMO approach converts this discrete problem into a continuous formulation where a design variable is introduced for each candidate orientation. Local constraints and penalization are then used to ensure that each subdomain is assigned a single orientation in the final solution. The subdomain over which orientation is constant is most simply defined as a finite element, ultimately leading to complex orientation layouts that may be difficult to manufacture. Recent literature has introduced threshold projections commonly used in density-based topology optimization into the DMO approach in order to influence the manufacturability of solutions. This work takes this idea one step further and utilizes the Heaviside projection method within DMO to provide formal control over the minimum length scale of structural features, holes, and patches of uniform orientation. The proposed approach is demonstrated on benchmark maximum stiffness design problems, and numerical results are near discrete with strict length scale control, providing a direct avenue to controlling the complexity of orientation layouts. This ultimately suggests that projection-based methods can play an important role in controlling the manufacturability of optimized material orientations.

Optimizing Topology and Fiber Orientations With Minimum Length Scale Control in Laminated Composites

Discrete Material Optimization (DMO) has proven to be an effective framework for optimizing the orientation of orthotropic laminate composite panels across a structural design domain. The typical design problem is one of maximizing stiffness by assigning a fiber orientation to each subdomain, where the orientation must be selected from a set of discrete magnitudes (e.g., 0°, ±45°, 90°). The DMO approach converts this discrete problem into a continuous formulation where a design variable is introduced for each candidate orientation. Local constraints and SIMP style penalization are then used to ensure each subdomain is assigned a single orientation in the final solution. The subdomain over which orientation is constant is typically defined as a finite element, ultimately leading to complex orientation layouts that may be difficult to manufacture. Recent literature has introduced threshold projections, originally developed for density-based topology optimization, into the DMO approach in order to influence the manufacturability of solutions. This work takes this idea one step further and utilizes the Heaviside Projection Method within DMO to provide formal control over the minimum length scale of structural features, holes, and patches of uniform orientation. The proposed approach is demonstrated on benchmark maximum stiffness design problems in terms of objective function, solution discreteness, and manufacturability. Numerical results suggest that projection-based methods can play an important role in controlling the manufacturability of optimized material distributions in optimized design and that solutions are near-discrete with performance properties comparable to designs without manufacturing considerations.